CAJ | 학술논문

岩土材料属于摩擦型材料,其强度特性时参数指标的选取至关重要.当前对剪胀角存在模糊认识,导致在理论分析和数值模拟分析中常会产生较大误差.在分析传统的滑移线场理论的基础上,采用广义塑性理论,证明了岩土材料在非关联流动法则条件下的剪胀角应取φ/2,且此时体变必为0.通过对具有精确理论解的经典Prandtl地基承载力课题的数值模拟分析,分别对关联流动法则、非关联流动法则剪胀角取φ/2及非关联流动法则剪胀角取0三种情况下地基的承载力进行了计算.结果表明,上述3种情况下得到的极限荷载的误差为2 %,但滑移线场与理论解有较大差异.其中,在非关联流动法则条件下,采用剪胀角ψ=φ/2所得到的滑移线场与Prandtl理论解一致,而采用ψ=0所得到的滑移线场与理论解有较大的偏差.这说明目前在非关联流动法则条件下采用ψ=0虽然可得到相应的正确的极限荷载,但是相应的滑移线场具有较大的误差,同时也证明了岩土材料在非关联流动法则条件下的剪胀角应该选取φ/2,而不是目前通常采用的0.
암토재료속우마찰형재료,기강도특성시삼수지표적선취지관중요.당전대전창각존재모호인식,도치재이론분석화수치모의분석중상회산생교대오차.재분석전통적활이선장이론적기출상,채용엄의소성이론,증명료암토재료재비관련류동법칙조건하적전창각응취φ/2,차차시체변필위0.통과대구유정학이론해적경전Prandtl지기승재력과제적수치모의분석,분별대관련류동법칙、비관련류동법칙전창각취φ/2급비관련류동법칙전창각취0삼충정황하지기적승재력진행료계산.결과표명,상술3충정황하득도적겁한하재적오차위2 %,단활이선장여이론해유교대차이.기중,재비관련류동법칙조건하,채용전창각ψ=φ/2소득도적활이선장여Prandtl이론해일치,이채용ψ=0소득도적활이선장여이론해유교대적편차.저설명목전재비관련류동법칙조건하채용ψ=0수연가득도상응적정학적겁한하재,단시상응적활이선장구유교대적오차,동시야증명료암토재료재비관련류동법칙조건하적전창각응해선취φ/2,이불시목전통상채용적0.
Geomaterials are factional materials, and their strength indexes play a key role in depicting strength characteristics. Illegible knowledge on dilatancy angle has existed for a long time, which caused large errors in theoretical analysis and numerical simulation. It was proved with the generalized geotechnical plastic mechanics principle that the angle of dilatancy should be φ/2 and the corresponding volumetric strain is zero for geomaterials under non-associated flow rule, based on traditional slip line theory. The classic foundation bearing capacity topic of Prandtl's solution, which has accurate theoretical interpretation, was analyzed systematically with step loading finite elements under the following three conditions: 1) associated flow rule, 2) non-associated flow rule with the dilatancy of φ/2 and 3) non-associated flow rule with the dilatancy of 0. Results showed that the errors of ultimate capacity obtained under the above three conditions were within 2 %, but the slip line fields were quite different. The slip line field obtained under-eonditon 2) was identical with that by Prandtl's solution, but a large deviation existed between condition 3) and Prandtl's solution. Thus a correct ultimate load and a slip line field with a great error can be acquired under condition 3), but both are precise under condition 2). Therefore, the angle of dilatancy should be φ/2, not 0 widely used at present when non-associated flow rule is applied.